Philosophia doesn't really change anything about how we heal. With a 3min CD, it's up so rarely that it's quite easy to just not use it. In the few instances where I do find myself using it (eg Enrage checks, Ion Cannon in M4S, etc), it's cool, but it doesn't change how I was handling that mechanic. If Ion Cannon existed in EW, or heck even in SHB, I would still do what I do now to deal with it. Philosophia is a 'win more' button IMO, where it just reinforces what you were already going to do to handle the mechanic (by increasing the healing of E.Prog by 150p effectively). Then, Psyche. Literally just 'press it on CD', no thought needed, 60s CD so it aligns with burst every time, etc.
By contrast, let's look at what I'm asking for WHM. At max level, Banish would be 370p with a 15s CD, compared to Glare3's 330p. This difference in potency is small enough that casting Glare instead of Banish is going to have zero effect on whether you clear or not. Additionally, because the 'average potency lost per GCD Banish is delayed' is about 6.6p, it allows for the player to purposely hold it, to use it for mobility, turning what would normally be a 330p loss for that 'mobility GCD' into a massive gain comparatively. I'd also change Dia to a 12s duration, such that A: it feels more 'bursty', B: it's used more often (so we have less Glare casts) and C: because it's used more often, that results in more instant-casts in the rotation (aids mobility).
Then, we look at the other button I'd add, Blessing of the Elementals. We add a 0-100 gauge, charged by casting non-Lily spells (healing GCDs charge it much faster). Glare is 1 point, Dia is 1 point each time it deals damage (both on cast and DOT for a total of 5 for its full duration), Banish is 5 points (because of the CD). Overall, this gives an estimated gauge gain of about 55 per minute, assuming you're casting zero 'bad' Healing GCDs. Spending 50 gauge on BOTE has two effects, A: it's a strong AOE healing action, and B: it grants a new gauge element, 'Elemental Petals'. When you have an Elemental Petal, the corresponding action on the hotbar (Glare/Dia/Banish) upgrades to Quake, Tornado, and Flood. The potencies of these Ultimate Elemental spells are balanced such that casting one of each is equal to 4 Glares, effectively making the gauge spender damage neutral. By adding a gauge gain rate to Holy, and making Quake/Flood/Tornado AOE, then we can also increase our 'dungeon trash button count' from one, all the way up to FIVE.
But wait, it gets better! We are all aware of how optimized WHM gameplay has us purposely 'waste' Lilies, so that we can put Misery into the 2min window, right? With this design, the same would be possible with Quake/Tornado/Flood. By wrangling the healing CD rotation correctly, a player would be able to turn their POM window into: POM, Flood, Tornado, Misery, Quake, Glare4, Flood, Tornado, Glare4, Glare4. And the best part is, the only hardcast in that entire window is the Quake, and it can be swapped with any of the Glare4s as needed! But at the same time, that 'optimization', of trying to put these actions in the raidbuff window, would be completely optional, just like how 'put Misery in raidbuffs' is completely optional right now. The difference in potency is so low that it would make no difference in hitting the enrage timer (if it would make/break the check, your party has bigger issues than 'healer didn't do the optimization thing'), and in parties that have few/no raidbuffs (eg VPR SAM MCH BLM) there's nothing to even line those 'refund' actions up with
And this by adding just two buttons to WHM. Two buttons, which can be made 'zero' by consolidating old trash buttons like Cure1 and Medica1 into their stronger counterparts (which we still want to avoid using, but not as much)